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https://doi.org/10.1016/j.wasman.2016.07.039

https://eprints.qut.edu.au/view/person/Skitmore,_Martin.html

https://eprints.qut.edu.au/98697/

https://doi.org/10.1016/j.wasman.2016.07.039

The S-curve for forecasting waste generation in construction projects

Weisheng Lu1, Yi Peng2,*, Xi Chen3, Martin Skitmore4, and Xiaoling Zhang5

1Associate Professor, Department of Real Estate and Construction, Faculty of Architecture,

The University of Hong Kong, Hong Kong, Email: [email protected]

2,*Corresponding author, Associate Professor, School of Public Administration, Zhejiang

University of Finance & Economics, Hangzhou, P.R. China. Tel.: (+86) 0571 8673 2303,

Email: [email protected]

3PhD Candidate, Department of Real Estate and Construction, Faculty of Architecture, The

University of Hong Kong, Hong Kong, Email: [email protected]

4Professor, Department of Construction and Project Management, Faculty of Science and

Engineering, Queensland University of Technology, Brisbane, Australia, Email:

[email protected]

5Associate Professor, Department of Public Policy, City University of Hong Kong, Hong

Kong, Email: [email protected]

mailto:[email protected]





The S-curve for forecasting waste generation in construction projects

Abstract

Forecasting construction waste generation is the yardstick of any effort by

policy-makers, researchers, practitioners and the like to manage construction and

demolition (C&D) waste. This paper develops and tests an S-curve model to indicate

accumulative waste generation as a project progresses. Using 37,148 disposal records

generated from 138 building projects in Hong Kong in four consecutive years from

Jan 2011 to June 2015, a wide range of potential S-curve models are examined, and as

a result, the formula that best fits the historical data set is found. The S-curve model is

then further linked to project characteristics using artificial neural networks (ANNs)

so that it can be used to forecast waste generation in future construction projects. It

was found that, amongst the S-curve models, cumulative logistic distribution is the

best formula to fit the historical data. Meanwhile, contract sum, location,

public-private nature, and duration can be used to forecast construction waste

generation. The study provides contractors with not only an S-curve model to forecast

overall waste generation before a project commences, but also with a detailed baseline

to benchmark and manage waste during the course of construction. The major

contribution of this paper is to the body of knowledge in the field of construction

waste generation forecasting. By examining it with an S-curve model, the study

elevates construction waste management to a level equivalent to project cost

management where the model has already been readily accepted as a standard tool.

Keywords: Construction waste management; Waste generation quantification;

Forecast; S-curve; Curve fitting;

1. Introduction

Construction and demolition (C&D) waste, sometimes simply referred to construction

waste, constitutes approximately 20%-30% of all waste worldwide (Srinivas, 2003).

Without proper management of C&D waste can result in severe degradation of the

environment (Lu and Tam, 2013; Boiral and Henri, 2012; Coelho and de Brito, 2012).

Construction projects, particularly sizable ones, generate a continuous stream of waste

that needs to be systematically planned and managed. This is increasingly becoming a

normative feature. For example, de Guzmán Báez et al. (2012) reported the Spanish

Government’s 105/2008 Royal Decree (Ministry of the Presidency, 2008), within

which the obligation to develop a waste management plan (WMP) in advance of each

construction project is of special interest. The WMP for a project site provides an

overall framework for waste management and reduction, and contains key types of

waste to be reduced, waste reduction targets, waste reduction programmes, waste

disposal procedures, and monitoring and audit (HKEPD, 2009). A WMP is also

mandated in economies such as the UK (Brian, 2008) and Hong Kong (HKDB, 2000)

for public works projects; failing to consider or comply with it as a legal duty means

the commitment of an offense that is punishable by law. In major economies, based on

the polluter pays principle, different C&D waste disposal charging schemes have been

enacted, whereby contractors are charged with a levy for every ton of waste they

dispose of, e.g. in landfills. Nowadays, it is not uncommon for contractors to put the

levy in their bids so that part of the extra cost will eventually be transferred to the

client. Hence, it is critical that both client and contractors have a relatively symmetric

access to the waste generation information to allow the contract to be fairly awarded.

During the course of construction, contractors need the information, e.g. to define the

size of roll-off containers, the best form of external and internal transport, and all the

waste logistics (Nagalli, 2013). Contractors also need to benchmark actual waste

generation against the WMP periodically so that appropriate interventions will be

introduced when necessary. In short, forecasting the construction waste generation

stream as a project progresses is pivotal in any effort to manage C&D waste.

Owing to its immediate material implications to construction waste management

(CWM), forecasting the generation of construction waste has become a hot research

topic, often under the umbrella of ‘quantifying waste generation’. Bergsdal et al.

(2007), Lu et al. (2015) and Lu et al. (2016) reported that forecasting C&D waste

generation could be at a project level, a regional level, and a national level. The

research reported in this paper is focused at the project level, although it could be used

for estimation at a regional level, e.g. by aggregating all the construction projects in

the region. Wu et al. (2014) reviewed C&D waste quantifying methods from the

perspectives of waste generation activity, estimation level, and quantification

methodology, and classified them into the following six types: site visit method, waste

generation rate method, lifetime analysis method, classification accumulation method,

variables modeling method, and other particular methods. Quantifying construction

waste generation can be conducted as a post-mortem of completed or ongoing projects,

e.g. by conducting on-site investigation (Lu et al., 2011), analysing waste disposal

records (Poon et al., 2004) or material flow (Cochran and Townsend, 2010; Li et al.,

2013), but its main thrust is to provide decision-making information for the future.

To provide this decision-making information, it is highly desirable to have a model

that can forecast waste generation as the project progresses, or even before the project

commences. Notably, de Guzmán Báez et al. (2012) used a linear model to forecast

the waste generation stream of Spanish railway projects determined by a few project

characteristics, such as length of the railway, and numbers of intersections and

underpasses. Cheng and Ma (2013) and Li et al. (2016) analysed waste generation by

investigating detailed design and construction units, e.g. work breakdown structure

and bills of quantities. Sáez et al. (2014) described the relationship between

accumulation of CDW in terms of weight or volume and durations with linear

regression with seven residential building projects. While the foregoing studies

sensibly emphasize the importance of investigating detailed units, they fall short of

providing a reliable waste generation rate (WGR), wastage levels, or conversion ratios

of materials to target products. Readers are thus encouraged to refer to the body of

references on WGR, which according to Lu et al. (2011) lies at the core of many

efforts for understanding waste management in the construction sector. Katz and

Baum (2011) developed a novel methodology to predict the accumulation of

construction waste based on field observations. According to Katz and Baum (2011),

waste “accumulates in an exponential manner”. This is clearly a very rough

approximation of the real situation, where the amount of waste tends to decrease

towards the end of projects as the finishing trades take over – suggesting a sigmoidal

or S-curve to be more appropriate. However, no previous research has attempted to

articulate the waste stream in this way.

The Project Management Institute (PMI) (2013) defines an S-curve as a graphic

display of cumulative costs, labour hours, percentage of work, or other quantities,

plotted against time. The name derives from the S-like shape of the curve (flatter at

the beginning and end, and steeper in the middle) produced on a project that starts

slowly, accelerates, and then tails off. The S-curve is particularly useful in project cost

management. For a project of n activities, the cost accruing at time point t is Ct, and

the accumulative cost ∑ 𝐶𝑡𝑛𝑡=1 for a regular project follows an S-curve as the project

progresses. Intuitively, the accumulative waste generated from the project should also

follow an S-curve. Once the curve is substantiated, it can be used to estimate the total

amount of construction waste generation, even during the preconstruction phase. This

information is very useful when contractors place the waste levy in their bids. The

S-curve can indicate specific accumulative waste generation at time point t and the

information is particularly useful for producing the WMP, e.g., in planning the site

area for temporarily storing the waste without conflicting with other trades, or

planning the transport for waste disposal. During the construction process, it can be

used as a baseline against which actual waste generation can be compared and

interventions introduced as necessary.

S-curve is a good tool to describe the accumulation of construction activities against

time. However, few studies, if not none, have used this tool to describe construction

waste generation. Therefore, construction waste management usually lacks effective

planning tools. The primary aim of this paper is to propose and test an S-curve for

forecasting construction waste generation by taking advantage of a big data set

formed by over five million waste disposal records generated from 9,850 projects in

Hong Kong from Jan 2011 to June 2015. It tends to provide contractors with not only

an S-curve model to forecast overall waste generation before a project commences,

but also with a detailed baseline to benchmark and manage waste during the course of

construction. The remainder of this paper is structured into five sections. Subsequent

to this first introductory section, the second section provides a literature review of

previous studies on the S-curve; the third section provides a detailed description of the

methodology, at the core of which is curve fitting by trial and error applied to big data

and artificial neural networks (ANNs); the fourth section presents the results and

findings; the fifth section discusses the results and findings; and the sixth and final

section draws a conclusion and makes suggestions for further related research.

2. The S-curve in project management

The S-curve is a graphic display of cumulative costs, labour hours, percentage of

work, or other quantities, plotted against time in a project (PMI, 2013). The shape of

the S-curve, normally with a smaller slope at the beginning and near the end and a

larger slope in the middle, indicates that progress is slower in initiation and closure of

resources but faster when the main work takes place. It is able to reveal the overall

project progress in single numbers. Early research works suggested the use of

cumulative plots of cost versus time and cumulative value versus time for project

control, and emphasized its role in facilitating senior managers to clearly understand

the overall financial situation. Cash flow forecasting based on S-curves was further

developed with more appreciation of financial management in construction in the

early 1970s (e.g. Hardy, 1970; Bromilow and Henderson, 1974; Balkau, 1975). Since

then, the use of S-curves has been an enduring research topic for project planning and

control, in forecasting cash flows in the preconstruction phase, and as targets to assess

the delay of actual progress in the construction stage (Chao and Chien, 2009).

There are some risks in using S-curves to establish the progress target for project

control. For example, under the threat of penalty for not meeting forecast values,

contractors may speed up non-urgent activities at the expense of critical activities

needed to achieve the targets (e.g. Jepson, 1969; Kim and Ballard, 2000). However, it

should be noted that S-curves provide a simple and handy tool with which project

managers can control projects; and the risks of misusing S-curves can be mitigated to

a certain extent by integrating them with other project management approaches, such

as milestone planning.

There are two approaches to generating S-curves for new projects considering the

information available for analysis. One is the schedule-based analysis that

accumulates the planned activity times and progress as shown by the formula in the

first row of Table 1, which is a brief summary of important mathematical formulas

adopted to estimate S-curves. The S-curves developed using this approach are usually

uneven due to irregular real-life data series (Chao and Chien, 2009). This approach is

only possible when the design and detailed project information is largely settled in

advance. The other approach is the historical-data-based estimation. As its name

indicates, S-curves developed in this way use data from completed construction

projects. The approach can be further divided into two types depending on whether it

has specific mathematic formulas. Type one is called envelop curves without specific

mathematical formula; curves are used to show the lower, mean, and upper limits of

cumulative project progress over time established according to a sample of completed

projects. The limited is pre-set by the planner (Kaka, 1999). Type two approach is to

characterize the relationship between progress and time with specific mathematical

formula. Different mathematical formulas are usually used to estimate the progress

along with time-based historical data. Since this study aims to forecast S-curve of

construction waste generation, type two approach using progress versus time relation

is adopted in the following investigations.

<<Please Insert Table 1 here>>

Two estimation methods can be used in the historical-data-based approach with

mathematic formulas. One is the nomothetic estimation, which generates a standard

S-curve as the basis for predicting the S-curve of a new project that can be classified

in the same category. Nomothetic estimation is based on nomothetic philosophy,

which tries to derive general laws and principles across categorized or

non-categorized groups of construction projects (Kenley and Wilson, 1989). Based on

previous studies (e.g. Hardy, 1970; Balkau, 1975; Bromilow and Henderson, 1977;

Drake, 1978; Hudson, 1978; Oliver, 1984; Singh and Woon, 1984; Miskawi, 1989;

Khosrowshahi, 1991), the typical analysis process of nomothetic estimation can be

summarized in the following steps: (1) collecting sufficient historical data of project

progress such as cost, value, relevant time, and general characteristics of the projects;

(2) classifying the projects into different groups according to their general

characteristics, e.g. through ANOVA analyses; (3) for each group, identifying the best

form of S-curve to fit the historical data of the individual projects; (4) generating a

standard S-curve for each project group, the parameters of which is the average value

of parameters of all the individual projects in the project group; (5) identifying the

best formula, i.e. the one that produces the smallest means square error (MSE) when

used for forecasting the historical project data, as different standard S-curves can be

generated from different selected formulae; and (6) using the standard S-curve as the

basis for prediction of a future project classified in that category.

The other method is the idiographic estimation, which produces an S-curve for a

specific project without generalizing it to other projects. Idiographic estimation is

based on the idiographic philosophy, which is devoted to understanding the meaning

of contingent, unique, and subjective phenomena (Thomae, 1999). The typical

analysis process of idiographic estimation can be summarized in the following steps:

(1) collecting sufficient historical data of project progress (cost/value), relevant time,

and general characteristics from existing projects; (2) identifying the best form of

S-curve to estimate the individual project; and (3) identifying the best formula, i.e. the

one that produces the smallest MSE when used for forecasting a future project.

Despite the difference in philosophy, there are some commonalities in the two

methods. Firstly, they both use curve fitting to identify the best formula among

available S-curve formulas to fit actual historical data (e.g. Skitmore, 1992). Secondly,

they use MSE as the criterion in identifying the best formula (e.g. Oliver, 1984; Singh

and Woon, 1984; Kenley and Wilson, 1989; Miskawi, 1989; Khosrowshahi, 1991;

Chao and Chien, 2009). However, researchers have questioned the nomothetic

estimation, as it is unreasonable to conduct a scientific investigation into an individual

and unique phenomenon (in social science) with the nomothetic approach in natural

science (De Groot, 1969; Runyan, 1983). As building projects are usually complex

and unique, it is often questionable to use a single and standard S-curve to represent a

certain type of project (Hudson and Maunick, 1974; Hudson, 1978). Therefore,

idiographic estimation has been increasingly emphasized as it can better reflect

historical data but its problem is the lack of the capability to predict cost or waste for

new projects (e.g. Thomae, 1999; Chao and Chien, 2009).

Researchers have further developed models to link S-curves (the parameter values of

determined S-curve formula) and project characteristics (e.g. contract sum, project

type) based on historical data by introducing methods such as artificial neural

networks (ANN) (e.g. Chao and Chien, 2009). ANNs are a family of models inspired

by biological neural networks (the central nervous systems of animals, the brain in

particular) and are used to estimate or approximate functions that can depend on a

large number of inputs and are generally unknown. Researchers such as Chao and

Skibniewski (1994), Boussabaine (1996), and Boussabaine and Kaka (1998), pointed

out that the capability of ANN to perform nonlinear mapping of output from multiple

inputs makes them suitable for handling estimation problems in construction that

typically involve complex input-output relations. This study follows this line of

inquiry to identify the link between the S-curve of construction waste generation and

project characteristics using the idiographic method and ANN.

3. Research methodology

After a detailed review of the literature on the S-curves, the methodology for

identifying the S-curve for forecasting construction waste generation (CWG) was

developed. The analytical process is illustrated in Figure 1.

<<Please Insert Figure 1 here>>

Step 1: Collecting historical data of time, relevant amount of construction waste,

and project characteristics

In this step, historical data of CWG and relevant project characteristics is collected

from completed projects. Construction waste disposal is used as a proxy of CWG, as

it is usually difficult to obtain on-site waste generation statistics every day but

comparatively feasible to access records of construction waste disposed at various

facilities such as landfills, as public departments in charge of these waste disposal

facilities normally maintain such records. For construction waste disposal, the time

point can be days, weeks or months, which may vary from one region’s practice to

another. Supposing the total number of projects under investigation is J, as a result of

this step, two sets of data of the jth project are collected as shown in Equations (1) and

(2):

𝑇𝑗 = {1,2,3, … , 𝐿𝑗} Equation (1)

𝐴𝑗 = {𝐴1𝑗 , 𝐴2𝑗 , 𝐴3𝑗 , … , 𝐴𝐿𝑗} Equation (2)

where 𝑇𝑗 is the time point set of the jth project, 1 is first time point of the jth project,

𝐿𝑗 is the total duration and also implies the number of data points of the jth project,

𝐴𝑗 is the data set of the construction waste disposal amounts by the jth project, 𝐴1𝑗

is the amount of construction waste disposal by the jth project at the first time point,

and 𝐴𝐿𝑗 is the amount of construction waste disposal by the jth project at 𝐿𝑗.

As an S-curve concerns cumulative progress at a specific time point, the data set 𝐴𝑗

should be further transformed to 𝐴𝐶𝑗 as shown in Equation (3):

𝐴𝐶𝑗 = {𝐴𝐶1𝑗 , 𝐴𝐶2𝑗 , 𝐴𝐶3𝑗 , … , 𝐴𝐶𝐿𝑗} = {𝐴1𝑗 , ∑ 𝐴𝑖=2𝑖=1 𝑖𝑗

, ∑ 𝐴𝑖=3𝑖=1 𝑖𝑗

, … , ∑ 𝐴𝑖=𝐿𝑖=1 𝑖𝑗

} Equation

(3)

where 𝐴𝐶𝑗 stands for the data set of cumulative amount of construction waste

disposal by the jth project, 𝐴𝐶1𝑗 is the cumulative amount of construction waste

disposal of the jth project at the first time point, and 𝐴𝐶𝐿𝑗 is the cumulative amount

of construction waste disposal of the jth project at 𝐿𝑗.

It stands to reason that large-scale projects (e.g. construction volume, or longer

duration) will normally generate more construction waste than small-scale

counterparts. In order to reduce the impact of project scale, the original data set is

standardized for further analyses. To this end, Equations (1) and (3) are standardized

in the form of Equations (4) and (5) respectively:

𝑇𝑆𝑗 = {𝑇𝑆1, 𝑇𝑆2, 𝑇𝑆3, … , 𝑇𝑆𝐿𝑗} = {1

𝐿𝑗,

2

𝐿𝑗,

3

𝐿𝑗, … ,1}Equation (4)

𝐴𝐶𝑆𝑗 = {𝐴𝐶𝑆1, 𝐴𝐶𝑆2, 𝐴𝐶𝑆3, … , 𝐴𝐶𝑆𝐿𝑗} = {𝐴𝐶1𝑗

𝐴𝐶𝐿𝑗,

𝐴𝐶2𝑗

𝐴𝐶𝐿𝑗,

𝐴𝐶3𝑗

𝐴𝐶𝐿𝑗, … ,1}Equation (5)

where 𝑇𝑆𝑗 denotes the data set of standardized time of the jth project, and 𝐴𝐶𝑆𝑗

denotes the data set of standardized cumulative amount of construction waste

generation of the jth project.

Apart from the time points and construction waste disposal amounts, the

characteristics of the project are also collected. According to existing studies of CWM

and S-curves (e.g. Lu and Yuan, 2010; Wang et al., 2010; Chao and Chien, 2009),

project characteristics such as duration, contract sum, location, project type, and client

type (e.g. private or public) are important in influencing CWG. To identify the full list

of project characteristics that has significant influences on CWG would deserve

another research paper(s). A wealth of research has been produced while it is still

largely inconclusive. This study roots itself in existing studies to identify the project

characteristics that matter. Another important consideration is the data availability.

Step 2: Identifying the best form of S-curve to model CWG

This step identifies an S-curve formula that best describes the data sets as shown in

Equations (4) and (5). Numerous S-curve models of cost and value have been

developed by previous studies. This study borrows such models to model a CWG

S-curve. A unique feature of this study is that a wide range of S-curves is examined in

order to find the one that best fits the data sets. This is possible given the

computational power available today. Software programs are designed in Matlab

(MathWorks, 2012) to conduct curve fitting so as to select the best-fit S-curve

formulas from the options as listed in Table 1.

Least-squares curve fitting analysis (LSCFA) is used to evaluate the fit of an S-curve

to the data of a specific project (Lu et al., 2013). The mean-square error (MSE) is

usually the specific indicator for the LSCFA, with:

𝑀𝑆𝐸𝑘𝑗 =∑ (𝐴𝐶𝑆𝑖𝑗−𝐴𝐶𝑆𝑖𝑗

𝑘 )2𝑖=𝐿𝑖=1

𝐿𝑗 Equation (6)

where 𝑀𝑆𝐸𝑘𝑗 denotes the MSE for the jth project when adopting the kth S-curve

formula for curve fitting, 𝐿𝑗 is the number of data points of the jth project, 𝐴𝐶𝑆𝑖𝑗 is

the real standardized cumulative amount of CWG of the jth project at the ith time

point, 𝐴𝐶𝑆𝑖𝑗𝑘 is the standardized cumulative amount of construction waste generation

of the jth project agreeing with the kth S-curve formula at the ith time point.

Based on Equation (6), the average MSE (AMSE) for all available projects when

adopting a specific S-curve formula is:

𝐴𝑀𝑆𝐸𝑘 =∑ 𝑀𝑆𝐸𝑘𝑗

𝑗=𝐽𝑗=1

𝐽 Equation (7)

where 𝐴𝑀𝑆𝐸𝑘 is the AMSE for all available projects when adopting the kth S-curve

formula, and J is the number of projects under consideration. The best S-curve

formula used to model the S-curve of CWG is the one that generates the minimal

AMSE.

Step 3: Establishing the link between project characteristics and parameter values

of CWG S-curve using ANN

As a single and standard S-curve is insufficient to forecast CWG in different projects

with different characteristics, a specific CWG S-curve needs to be developed by

linking the standard CWG curve with the project characteristics. No previous research

has been conducted to explore this link. Neither is it clear whether the link is linear or

not. Nevertheless, existing studies have demonstrated that there is a complex and

non-linear relationship between the cost S-curve and project characteristics (e.g. Chao

and Chien, 2009). ANNs are capable of investigating complex, non-linear, or even

unknown effects of inputs on outputs. They have also proved to be useful in

determining a specific cost S-curve in construction projects and are therefore adopted

in this study.

An ANN takes the link between inputs and outputs as a black box, while relying on

training data to find the connection structure and weights that best reflect the nexus

between inputs and outputs. With real input data (project characteristics in this case)

and output data (parameter values of CWG S-curve of existing projects), a

feed-forward multilayer network and a supervised learning technique, such as the

gradient descent back-propagation (BP) algorithm, are usually adopted for training.

The genetic algorithm (GA) performs better in determining the weighting and

threshold of ANN models and is therefore combined with BP to develop this study's

ANN model. No previous understanding has been gained on the project characteristics

that impact a CWG S-curve and therefore an explorative study is used to examine the

different combinations of project characteristics as the input variables. The ANN

model based on the combination of characteristics that generates the lowest MSE

finally determines the ANN model for future forecasting. The detailed algorithm of

the ANN model development for this study is illustrated in Figure 2 by referring to

Chinese Matlab Forum (2010).


Two-thirds of the real-life data collected is randomly selected for training the model.

In order to avoid overtraining, the available training data is further randomly divided

into two groups (Chao and Chien, 2009). Training terminates when the MSE of the

real-life data and forecast data reach the preset criteria, such as 5%. In addition,

one-third of remaining real-life data is randomly divided into two groups to test the

performance of the trained model. Such division is a preferred approach to test the

suitability of the trained model by avoiding over-fitting problem, which is widely

existed in ANN (Chao and Chien, 2009). As shown in Figure 3, the ANN model is

determined by its weights, which are adjusted during the training process until the

pre-set criteria are satisfied.

After this step, an ANN model that describes the link between project characteristics

and parameter values of the CWG S-curve is developed. The ANN model is then used

for forecasting the CWG S-curve of a new project in the next step.


Step 4: Forecasting CWG by applying the S-curve to new projects with different

characteristics

With the developed model in this study, CWG S-curve of new projects can be forecast

at the preconstruction phase when the characteristics information of the projects is

largely ready. The project characteristics of the new projects can be determined by the

contractor reasonable estimation. With the input of project characteristics, the neural

network developed in Step 3 can determine the value of parameters of the identified

S-curve formula. Finally, CWG S-curve of new projects can be drawn with the

parameter value and identified S-curve formula.

4. Data analyses and results

The S-curve for forecasting the waste generation from construction projects is

contextualised in Hong Kong. The Construction Waste Disposal Charging Scheme has

been enacted to effectively manage C&D waste in Hong Kong since 2006. This

involves construction contractors disposing of construction waste in designated

facilities such as landfills or public fill, with a waste disposal charging fee being

applied for the waste delivered to the facilities. The Hong Kong Environment

Protection Department (HKEPD) manages the facilities and also maintains the record

of every truckload of construction waste received at a designated facility. The scheme

led to the creation of a big data set containing 5,631,539 disposal records generated

from 9,850 projects from January 2011 to June 2015. Figure 4 is a screenshot of some

typical records included in the big data. Every waste disposal record contains the date

of a transaction, the vehicle number, the amount of the construction waste (weight-in,

weight-out and net weight), time-in and time-out, and the account number of the

corresponding construction project. Using the account numbers, the disposal records

are linked to another relational database where project information is stored, such as

contract sum, construction type, site address, and client type (see Figure 5).



This big data is expected to allow a CWG S-curve model to be trained and tested so

that the model is able to provide adequate forecasts of the progressive waste

generation of new construction projects. Since the study aims at discovering

underlying patterns in the cumulative amount of construction waste disposal (𝐴𝐶𝐿𝑗)

changes over time for waste disposal (𝐿𝑗) of construction work, an S-curve describing

the change of 𝐴𝐶𝐿𝑗 with 𝐿𝑗 is drawn for each project by identifying the best form

among existing S-curve formulas. Various construction types, such as buildings,

demolition, substructures and civil projects are involved in the four years’

construction waste disposal transactions. Building projects, which are the most typical

construction type in the data set, are selected to develop the S-curve model.

Furthermore, some of the outliers are eliminated before model development. The

building projects should comply with the following criteria:

(1) To stay within the scope of the data, the projects should start to generate

waste between 31 Jan 2011 and 30 June 2014;

(2) To avoid non-typical projects (e.g. minor maintenance works), the

construction waste disposal activities should last more than 30 days; and

(3) To provide a sufficient number of data points for fitting the S-curve, the

construction waste should be produced on at least 20 single days.

These resulted in 138 building projects with 37,148 disposal records meeting the

criteria. By following Steps 1 and 3, the nine analytical S-curve models listed in Table

1 are used to fit the data of the 138 projects. Table 2 summarizes the results, which

show that P6, a cumulative logistic distribution developed by Skitmore (1998),

generates the smallest average MSE (see Equation 7 and Table 2). Therefore, the best

S-curve form used for fitting the CWG S-curve is:

y =𝑒𝑎+𝑏𝑥

1+𝑒𝑎+𝑏𝑥 Equation (8)

where x is the standardized time and y is the standardized amount of generated

construction waste.


Taking one of the projects (Project no. 7018343) as an example, when using P6 to fit

the CWG S-curve, the fitting form is:

y =𝑒−3.3548+11.5191𝑥

1+𝑒−3.3548+11.5191𝑥 Equation (9)

The MSE of this fitting is 0.17%. Figure 6 is an illustration of the real-life data and

fitted curve.


After the best S-curve formula to fit the CWG S-curve is determined, ANN is used to

link the project characteristics and the parameter values, i.e. a and b in Equation (8).

Unlike Equation (8) for a very specific project, the a and b in Equation (8) should fit a

group of projects. Table 3 is a statistical summary of the project characteristics and

parameter values.


The data points from 100 of the projects are used in ANN model development through

training and the remaining 38 used for model test. In order to reduce data bias, two

sets (designated as Modeling Samples 1 and 2, each with 50 projects in it) while two

testing groups (designated as Testing Samples 1 and 2, each with 19 projects) are

randomly picked from the 138 projects (Chao and Chien, 2009). Moreover, in order to

alleviate potential data distortion, this study standardized the value of original contract

sum and duration to be between 0 and 1 according to respective maximum value

(Chao and Chien, 2009).

Firstly, an initial configuration is chosen of neural networks of four input nodes,

which is the number of input project characteristics, ten nodes in one hidden layer,

two output nodes in the output layer, a learning rate of 0.1, and the log-sigmoid

transfer function according to Chao and Chien (2009). For parameter setting of GA,

the cross probability is 0.4, the mutation probability is 0.2, the size of the population

is 20, and the maximum generation (maximum number of iterations of the GA process)

is 200. The initial configuration of GA and the operation program is based on Chinese

Matlab Forum (2010). Each network’s performance is then evaluated by the AMSE as

specified in Equation (7). According to Chao and Chien (2009), a few adjustments

and trials were made and the final configuration was revised to learning rate of 0.7

and seven nodes in the hidden layer in order to improve the performance of ANN.

Using the ANN model, different combinations of project characteristics are tried. In

the experimental study, four project characteristics, namely duration, public-private

nature, location, and contract sum are available. In order to have a good explanation,

at least three project characteristics should be considered, which means there are five

combinations as shown in Table 4. After selecting the combinations of project

characteristics, the ANN model would be rerun according to the steps as mentioned

above.

As specified in Step 3, one set of fifty projects was randomly selected in training

samples 1 and 2 while another set of nineteen projects was randomly selected in

testing samples 1 and 2 in order to avoid the overtraining problem existed in ANN.

Table 4 is a statistical summary of the MSE of the ANN model. For example, the

mean MSE of fifty projects in training sample 1 is 4.55%, based on the input of ANN

model as project characteristics combination of contract sum, location, public-private

nature, and duration. If the input of the ANN model is a combination of project

characteristics such as contract sum, public-private nature, and duration, the mean

MSE of fifty projects in training sample 1 is 9.61%. It can be found that a

combination of contract sum, location, public-private nature, and duration generates

the lowest MSE for all samples. Therefore, the combination of contract sum, location,

public-private nature, and duration is finally selected as the input of the ANN model

for further analysis. For the combination of contract sum, location, public-private

nature, and duration, it is found that the mean MSE of training samples 1 and 2 and

testing samples 1 and 2 are different. Such difference demonstrates that the ANN

model has different explanation for different samples. If training samples 1 and 2 are

combined for training the model while testing samples 1 and 2 are combined for

testing the model, the mean MSE of the training sample and testing sample would be

lowered due to overtraining and over-fitting (Chao and Chien, 2009). Therefore, the

results would be twisted without such divisions; it is thus a sensible strategy to divide

training samples and testing samples if the sample is sufficient.


Under the best combination of project characteristics, the mean value of MSE of all

samples is below 5% while the median value of MSE of all samples is below 3.98.

The statistical results demonstrate that the forecast of CWG S-curve through the ANN

model is acceptable. One of the projects in testing sample 1 is used for illustration.

Equation (10) illustrates the CWG S-curve, the parameters of which were obtained

from the ANN model. The MSE of this forecast is 0.23%. Figure 7 compares the

real-life data and CWG S-curve forecast by the ANN model for this project (Project

no. 7018343).

y =𝑒−3.2560+10.1916𝑥

1+𝑒−3.2560+10.1916𝑥 Equation (10)


5. Discussion

This research provides useful references for both industry practitioners and academic

researchers in exploring construction waste management.

5.1 Relevance to industry practitioners

As this research relies on detailed project information mined from real-scenario ‘big

data’, the methodology, using the cumulative logistic distribution for progress

generalization and ANN model, provides an ideal schedule-based progress estimate

for construction control and gives early estimates for decision-makers (i.e. estimators

or project managers). In project management schemes, project characteristics are

normally stated before the commencement of a construction project. With the input of

characteristics including estimated contract sum, site location, and estimated

construction duration, the methodology is a potentially useful tool for forecasting the

waste generation amount and progress of building projects, thereby bringing various

benefits to multiple parties involved in CWM. The S-curve can indicate specific

accumulative waste generation at a concerned time point and the information is

particularly useful for producing the WMP, e.g., in planning the site area for

temporarily storing the waste without conflicting with other trades, or planning the

transport for waste disposal. During the construction process, it can be used as a

baseline against which actual waste generation can be compared and interventions

introduced as necessary. These benefits are as follows:

(1) For project contractors/managers, the model can predict a baseline S-curve to

be used for estimating the waste management requirements, such as disposal

amount, vehicle amount, piling space, and duty scheduling during construction

progress.

(2) At the project planning stage, the CWG S-curve based on the model not only

provides consultants with the predicted total waste generation amount, but also

indicates construction progress through estimating waste generation progress,

so that contractors can estimate financing requirements and personnel demand

at different construction stages. For example, by estimating the construction

peak of a project from the duration when waste amount soars in the forecast

curve, a contractor may allocate more human and financial resources at the

peak.

(3) As it is developed from previous building cases, the model can provide

decision-makers, such as public policy-makers and building project

contractors, with a baseline to benchmark waste generation amounts for future

construction works.

(4) Stakeholders in CWM as a whole may utilize this model as a reference to

develop a standard and handy tool to be accepted by the construction industry

for predicting CWG progress.

5.2 Challenges in applying the CWG S-curve model

Compared with existing studies, the S-curve model provides a simple and handy tool

with which project managers can conduct construction waste management. However,

this model should be integrated with other construction waste management tools like

field investigation to deal with the possible variations between the forecast and

real-life waste generation amounts. It should be noticed that the results from this study

have certain limitations in application to other projects and areas. The constraints of

generation include unforeseen changes in construction projects, other project

characteristics affecting CWG, city location of projects, and differences of

construction waste management schemes.

Inherently, the accuracy of forecasting the future is open to question, even though the

model developed from this study fits the historical data and the case study shows its

robustness. Unforeseen changes of construction projects occur frequently, for instance,

the emergence of a new construction technology that can systematically reduce CWG

across the whole industry, the utilization of new light materials that can bring down

the weight of construction waste by a large margin, or the wide adoption of

prefabricated members that can sharply mitigate waste generation on site. All these

changes will have significant impacts on CWG, hence deviating the estimated S-curve

in reality. This study only identifies four project characteristics, namely, contract sum,

location, public-private nature, and duration as the determinants of CWG. They are

used for deriving parameters of S-curves from the ANN model. Other project

characteristics when they are reported as impactful and their data is available, should

be considered to develop the S-curve formula and ANN model for the purpose of

developing more accurate CWG S-curves.

The CWG S-curve is developed in the context of Hong Kong, which is a small but

highly condensed territory having a multitude of high-rise buildings with many

standard repetitive floors. It is, therefore, reasonable to predict the total waste amount

generated from building projects constructed in highly condensed and well-developed

regions that predominantly use steel and concrete composite structure. However, this

model should be treated with caution when applied to other scenarios, e.g. villas or

low-rise building projects, which are commonly seen in countries with small

populations but relatively large territories. As the quantity and quality of materials

(e.g. rebar, concrete, bricks, stone) used in low-rise and high-rise structures are greatly

different, the waste material amount and type will likely be different for developing

the CWG S-curve.

Even in New York, London, Singapore, Tokyo and other places with a large volume

of high-rise buildings with similar characteristics to Hong Kong, sufficient caution

should be given before predicting waste generation. The differences of construction

management schemes (e.g. major structural or finishes materials, or schedule of

construction stages) should be considered when forecasting waste generation. For

example, the S-curve may also ‘twist’ with the volume of the on-site buffer for

construction waste and the construction progress schedules, which may vary with

construction management regulations of specific economies. Although there are

certain risks associated with using the S-curve formula and ANN model developed in

this study to calculate progress S-curves for cases and jurisdictions that are not similar

to those in this study, the research logic is replicable, and is hopefully replicated for

developing CWG S-curves in future studies.

6. Conclusions and future studies

Forecasting construction waste generation as the project proceeds is the cornerstone of

any effort to manage C&D waste, e.g. pricing construction waste disposal in bidding,

benchmarking actual waste generation, introducing construction waste management

interventions, and planning external and internal transport and all the waste logistics

during the course of construction. This research contributes to previous studies

relating to the forecasting of construction waste generation, by offering and testing an

S-curve to indicate accumulative waste generation as a project progresses. Benefiting

from good data availability, and using curve fitting and artificial neural networks

(ANNs), this research found the existence of such an S-curve. By inputting

information relating the four project characteristics of contract sum, location,

public-private nature, and duration, the S-curve model can satisfactorily forecast

waste generation in new construction projects. The S-curve, therefore, provides more

scientific evidence for construction waste management.

However, the specific S-curve function identified in this study might not stand in

contexts other than the one in which it was developed, i.e. high-rise buildings in Hong

Kong predominantly adopting a steel-concrete composite structure. Nevertheless, this

study provides an undeniably robust methodology to develop CWG S-curves so that

researchers can replicate it and develop CWG S-curves suitable for their own context.

It would also be meaningful to investigate CWG S-curves by considering more

project characteristics, such as building height. Furthermore, it is recommended to

develop an overall S-curve formula and ANN model for other types of projects (e.g.

civil, demolition, foundation, maintenance, and renovation). By following the same

methodology, future studies are also recommended to consider unforeseen changes

such as new building technologies, new materials, or adoption of prefabricated

members, with a view to developing a more accurate estimation of waste generation

in construction projects.

7. Acknowledgement

The research was supported by the National Nature Science Foundation of China

(NSFC) (Project no.: 71273219).

Abbreviations list

C&D waste: construction and demolition (C&D) waste

ANNs: artificial neural networks

WMP: waste management plan

CWM: construction waste management

WGR: waste generation rate

MSE: means square error

CWG: construction waste generation

AMSE: average MSE

BP: back-propagation

GA: genetic algorithm

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Step 1

Step 2

Step 3

Step 4

Figure 1 The research methodology for deriving construction waste generation

S-curves

Collecting historical data of time, relevant amount of construction waste, and project characteristics

Identifying the best form among existing S-curve formulas to

model CWG S-curve

Establishing the link between project characteristics and

parameter values of CWG S-curve using neural networks

Forecasting CWG for new construction projects using the

S-curve

Standardized time and amount of construction waste; and

Project characteristics including contract sum, duration, type of project and location

Curve-fitting using existing S-curve formulas to all projects.

The best form is the one that generates the smallest MSE when estimating based on the historical data; and

Determining specific parameter values of the best form for each project.

Input: important project characteristics; output: parameter values of the CWG S-curve; and process: one-hidden layer neural networks, two-thirds of historical projects used for establishing the neural networks; and one-third of historical projects used for testing the neural networks.

Forecasting the parameter values of CWG S-curve with established neural networks and project characteristics of new projects; and Drawing CWG S-curve based on parameter values for CWM of new projects.

Initial GA coding

Determine the BP structure

according to combination

of input variables

Initialize the weighting and

threshold of BP

Data input

Data

standardization

Using the trainded

error of BP as fitness

index

Selection operation

Cross operation

Mutation operation

Calculating the fitness

index

Reach max

number of

iterations?

Obtaining best weighting

and threshold of BP

Calculating the trained

error of BP

Updating the weighting and

threshold of BP

Reach the

preset

objectives?

Forecasting with

determined BP

All combinatons

of input

variables?

Calculating MSE of

forecasted CW S-curve

Selecting the combination

of input variables

generating lowest MSE

No

Yes

No

Yes

Yes

No

Figure 2 The process of determining specific CWG S-curve using ANN

Figure 3 The structure of the ANN model

Input layer:

standardized project

characteristics

of training sample

Output layer:

parameter value of determined CWG S curve

contract sum

duration

...

Hidden layer

a

b

... ...

adjust weighting through training

Weighting Weighting

Figure 4 Screenshot of some typical transaction records in the set of ‘big data’

Figure 5 Screenshot of ‘account details’ of projects disposing of construction waste

Figure 6 Comparison of the real-life data and fitted curve using P6 to fit one of the

projects as an example

Figure 7 Comparison of real-life data and the CWG S-curve forecast by the ANN

model for Project no. 7018343

Table 1 Summary of modelling for estimating S-curves

Type Sub-type Formula Remarks References

Schedule-based S1 𝑃𝑡 = ∑ 𝑤𝑖 × 𝑝𝑡𝑖

𝑛

𝑖=1

Design and detailed project information is available

Chao and Chien (2009)

Historical data and empirical method

H1 Envelop curves without specific mathematical formula

Curves are used to show the lower, mean and upper limits of cumulative project progress over time established according to a sample of completed projects. The limited is pre-set by the planner

Kaka (1999)

Progress versus-time relation

P1 𝑦 = 𝑥 + 𝑎𝑥2 − 𝑎𝑥− (6𝑥3

− 9𝑥2

+ 3𝑥)/𝑏

a, b can be evaluated using the Weibull function according to the contract value

Hudson, 1978; Tucker,1988

P2 ln [𝑦/(1 − 𝑦)] = 𝑎+ 𝑏{ln [𝑥/(1− 𝑥)]}

a, b can be obtained through a linear regression analysis with transformed data set. The first 10% and final 10% of progress data from the set should be excluded for analysis.

Kenley and Wilson (1989)

P3 y = [1 + 𝑎(1 − 𝑥)(𝑥− 𝑏)]𝑥

a, b for given project progress data can be obtained through trial-and-error method by matching the right-hand and left-hand sides

Berny and Howes, 1982

P4 y = 𝑎𝑥3 + 𝑏𝑥2 + (1 − 𝑎− 𝑏)𝑥

a, b can be obtained through the least-squared error method with the historical data, which can further be forecast by contract amount, duration, type of work, and location using neural networks.

Chao and Chien (2009)

P5 y = erf (𝑥 − 𝑎

𝑏) Cumulative normal

distribution Skitmore (1998)

P6 y =

𝑒𝑎+𝑏𝑥

1 + 𝑒𝑎+𝑏𝑥 Cumulative logistic distribution

Skitmore (1998)

P7 y = erf (

𝑙𝑛𝑥 − 𝑎

𝑏)

Cumulative lognormal distribution

Skitmore (1998)

where wi=percent weight of activity i in the project; pti=percent complete of activity i

at t. x is the standardized time range between 0 and 1, y is the standardized

cost/progress range between 0 and 1. erf is the cumulative normal probability

function.

Table 2 Statistical summary of the MSE

Statistics of MSE P1 P2 P3 P4 P5 P6 P7

Mean 0.0121 0.1221 0.008 0.0049 0.0077 0.0043 0.0339

Median 0.0096 0.1121 0.0041 0.0034 0.0063 0.0032 0.0284

Standard

Deviation (SD) 0.0105 0.0634 0.0111 0.006 0.0058 0.0037 0.0478

Table 3 Statistical summary of the project characteristics and parameter values

Group

number

(location)

Number

of

projects

Mean value of

contract sum

(HKD)

Mean

value of

duration

(days)

Mean value of

project

type(1=public,

0=private)

Mean

value of

parameter

a

Mean

value of

parameter

b

1(NT) 43 284104398.91 713.40 0.12 -3.1931 65.8094

2 (KL) 51 210461785.11 747.72 0.14 -2.9052 42.9622

3(HK) 44 242472233.72 788.93 0.02 -3.0683 17.3411

NT=New Territories, KL=Kowloon, and HK=Hong Kong Island

Table 4 Statistical summary of MSE of the ANN model (%)

Project characteristics ANN Sample Mean SD Median

Contract sum, location, public-private

nature and duration

Modeling sample 1 4.55 3.73 3.35


Testing sample 1 4.68 4.46 2.99


Contract sum, public-private nature

and-duration





Contract sum, location and duration Modeling sample 1 8.87 8.59 5.62




Location, public-private nature and

duration




Testing sample 2 10.59 10.62 5.55

Contract sum, location and public-private

nature





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